Green [J. Acoust. Soc. Am. 87, 2662-2674 (1990)] suggested an efficient, maximum-likelihood-based approach for adaptively estimating thresholds. Such procedures determine the signal strength on each trial by first identifying the most likely psychometric functions among the pre-proposed alternatives based on responses from previous trials, and then finding the signal strength at the "sweet point" on that most likely function. The sweet point is the point on the psychometric function that is associated with the minimum expected variance. Here, that procedure is extended to reduce poor estimates that result from lapses in attention. The sweet points for the threshold, slope, and lapse parameters of a transformed logistic psychometric function are derived. In addition, alternative stimulus placement algorithms are considered. The result is a relatively fast and robust estimation of a three-parameter psychometric function.